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%I #5 Oct 31 2013 12:17:32
%S 1,1,2,6,3,15,5,35,35,105,7,77,77,1001,143,429,2145,36465,12155,
%T 230945,46189,323323,29393,676039,676039,16900975,1300075,2340135,
%U 334305,9694845,215441,6678671,100180065,3305942145,64822395,2268783825
%N Divide n! repeatedly by i! for i from floor(n/2) down through 2; a(n) = remaining quotient.
%e a(9): 9!/(4!*4!*3!) = 105.
%t f[n_] := Block[{k = Floor[n/2], m = n!}, While[k > 1, While[ Mod[m, k! ] == 0, m /= k! ]; k-- ]; m]; Table[ f[n], {n, 0, 35}] (* _Robert G. Wilson v_ *)
%o (PARI) a(n)=c=n!;forstep(d=floor(n/2),2,-1, while (c%(d!)==0,c/=d!));c
%Y Cf. A055773.
%K nonn
%O 0,3
%A _Jon Perry_, Nov 23 2005
%E More terms from _Robert G. Wilson v_, Nov 25 2005